A Hard 7×7 Puzzle Solved with Forced Chain in 17 Steps
Play this board yourself →A
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This 7×7 board rates as hard (difficulty score 981). Solving it from scratch takes 17 logical steps, using 8 techniques: Single cell, Row/column exclusion, Adjacency clear, Region confinement, Line confinement, Paired regions, Shape squeeze, Forced chain. Every step below is forced: nothing here is a guess.
- First, every open cell left in this region sits in column A, so its marker has to land there; that clears every other open cell in the column.
- Next, together, two regions have open cells only in columns B and C; with one marker each, those two markers have to fill exactly those two columns, so every other region's open cells there can be cleared.
- Then, every open cell left in this region sits in column D, so its marker has to land there; that clears every other open cell in the column.
- After that, every remaining candidate in this region touches B2 and C2, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Now, every remaining candidate in this region touches B3, so whichever candidate ends up marked will clear it, and it can be ruled out now regardless of which one wins.
- From there, every open cell left in this region sits in row 1, so its marker has to land there; that clears every other open cell in the row.
- Following that, every open cell left in this region sits in row 2, so its marker has to land there; that clears every other open cell in the row.
- First, every open cell in column G belongs to the same region, so that region's marker has to be somewhere in this column; that clears every other open cell in the region.
- Next, every remaining candidate in this region touches C4 and E5, so whichever candidate ends up marked will clear them, and they can be ruled out now regardless of which one wins.
- Then, that one can't be the marker: at C1 it would force B4 (the last open cell in region 3), then D5 (the last open cell in region 5), then E7 (the last open cell in region 7), and the chain continues, and row 3 would be left with no open cell for its marker.
- After that, place a marker at B1. Region has exactly one open cell left. Placing here clears the rest of row 1, column B, and its region.
- Now, place a marker at C3. Region has exactly one open cell left. Placing here clears the rest of row 3, column C, and its region. Placing here also clears its 1 touching neighbour.
- From there, place a marker at D5. Region has exactly one open cell left. Placing here clears the rest of row 5, column D, and its region. Placing here also clears its 1 touching neighbour.
- Following that, place a marker at E7. Region has exactly one open cell left. Placing here clears the rest of row 7, column E, and its region.
- First, place a marker at F2. Region has exactly one open cell left.
- Next, place a marker at A6. Region has exactly one open cell left. Placing here clears the rest of row 6, column A, and its region.
- Finally, place a marker at G4. Region has exactly one open cell left.
The key move here was Forced chain. Once you can spot that, this board falls quickly. ∎